What Are Complex Numbers?

What do you get when you put a real and an imaginary number together? A complex number. No, not a complicated number (although it is kind of complicated). We’re talking about an entirely new set of numbers dubbed “complex”

The world of math is complex … in more ways than one. Sure, it’s full of complex ideas that are all tied up and packaged within beautiful and often times complex wrapping paper that is adorned with complex looking mathematical symbols.

But it’s also literally complex … by which I mean it’s built upon a fundamental set of numbers called complex numbers. Wait, yet another type of number? Yep! You know all about real numbers, and last time we dove deep into the pool of imaginary numbers, but there is one more set of numbers for you to wrap your head around—they’re called complex numbers.

What are they? How should you think about them? And what can you do with them? Those are exactly the questions we’ll be talking about today.

Real and Imaginary Numbers

In one sense all numbers are “real.” After all, I’m real and I’m thinking about them … so they’re certainly real to me. But as we’ve discussed before, only some numbers are really real. And that’s because the word “real” has a particular meaning in math. Real numbers are all the numbers you can find on a real number line. That means that real numbers include zero and the other integers, all the rest of the rational numbers, and each and every one of the infinity of irrational numbers, too.

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